On the isoperimetric problem in Euclidean space with density
微分几何
2007-05-23 v1
摘要
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally, we prove this conjecture and the uniqueness of minimizers for the density by using symmetrization techniques.
关键词
引用
@article{arxiv.math/0602135,
title = {On the isoperimetric problem in Euclidean space with density},
author = {César Rosales and Antonio Cañete and Vincent Bayle and Frank Morgan},
journal= {arXiv preprint arXiv:math/0602135},
year = {2007}
}
备注
19 pages, 3 figures